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Efficient Estimation of Semiparametric Transformation Models for Two-Phase Cohort Studies

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  • Donglin Zeng
  • D. Y. Lin

Abstract

Under two-phase cohort designs, such as case--cohort and nested case--control sampling, information on observed event times, event indicators, and inexpensive covariates is collected in the first phase, and the first-phase information is used to select subjects for measurements of expensive covariates in the second phase; inexpensive covariates are also used in the data analysis to control for confounding and to evaluate interactions. This article provides efficient estimation of semiparametric transformation models for such designs, accommodating both discrete and continuous covariates, and allowing inexpensive and expensive covariates to be correlated. The estimation is based on the maximization of a modified nonparametric likelihood function through a generalization of the expectation--maximization algorithm. The resulting estimators are shown to be consistent, asymptotically normal and asymptotically efficient with easily estimated variances. Simulation studies demonstrate that the asymptotic approximations are accurate in practical situations. Empirical data from Wilms' tumor studies and the Atherosclerosis Risk in Communities (ARIC) study are presented. Supplementary materials for this article are available online.

Suggested Citation

  • Donglin Zeng & D. Y. Lin, 2014. "Efficient Estimation of Semiparametric Transformation Models for Two-Phase Cohort Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 371-383, March.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:505:p:371-383
    DOI: 10.1080/01621459.2013.842172
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    Cited by:

    1. Ying Yan & Haibo Zhou & Jianwen Cai, 2017. "Improving efficiency of parameter estimation in case-cohort studies with multivariate failure time data," Biometrics, The International Biometric Society, vol. 73(3), pages 1042-1052, September.
    2. Yei Eun Shin & Ruth M. Pfeiffer & Barry I. Graubard & Mitchell H. Gail, 2020. "Weight calibration to improve the efficiency of pure risk estimates from case‐control samples nested in a cohort," Biometrics, The International Biometric Society, vol. 76(4), pages 1087-1097, December.
    3. Yayun Xu & Soyoung Kim & Mei-Jie Zhang & David Couper & Kwang Woo Ahn, 2022. "Competing risks regression models with covariates-adjusted censoring weight under the generalized case-cohort design," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(2), pages 241-262, April.
    4. Suhyun Kang & Wenbin Lu & Mengling Liu, 2017. "Efficient estimation for accelerated failure time model under case-cohort and nested case-control sampling," Biometrics, The International Biometric Society, vol. 73(1), pages 114-123, March.
    5. Jon Arni Steingrimsson & Robert L. Strawderman, 2017. "Estimation in the Semiparametric Accelerated Failure Time Model With Missing Covariates: Improving Efficiency Through Augmentation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1221-1235, July.
    6. Qingning Zhou & Jianwen Cai & Haibo Zhou, 2018. "Outcome†dependent sampling with interval†censored failure time data," Biometrics, The International Biometric Society, vol. 74(1), pages 58-67, March.
    7. Deng, Lifeng & Ding, Jieli & Liu, Yanyan & Wei, Chengdong, 2018. "Regression analysis for the proportional hazards model with parameter constraints under case-cohort design," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 194-206.
    8. Mingzhe Wu & Ming Zheng & Wen Yu & Ruofan Wu, 2018. "Estimation and variable selection for semiparametric transformation models under a more efficient cohort sampling design," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 570-596, September.
    9. Lin, Chanjuan & Zheng, Ming & Yu, Wen & Wu, Mingzhe, 2019. "Robust inference for the proportional hazards model with two-phase cohort sampling data," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 98-103.
    10. Qingning Zhou & Jianwen Cai & Haibo Zhou, 2020. "Semiparametric inference for a two-stage outcome-dependent sampling design with interval-censored failure time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 85-108, January.
    11. Jing Zhang & Haibo Zhou & Yanyan Liu & Jianwen Cai, 2021. "Feature screening for case‐cohort studies with failure time outcome," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 349-370, March.
    12. J. F. Lawless, 2018. "Two-phase outcome-dependent studies for failure times and testing for effects of expensive covariates," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 28-44, January.
    13. Han, Bo & Wang, Xiaoguang, 2020. "Semiparametric estimation for the non-mixture cure model in case-cohort and nested case-control studies," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    14. Jing Zhang & Haibo Zhou & Yanyan Liu & Jianwen Cai, 2021. "Conditional screening for ultrahigh-dimensional survival data in case-cohort studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 632-661, October.

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